Question: A circle has a sector with area $\dfrac{3}{2}\pi$ and central angle $60^\circ$. What is the area of the circle? {9\pi} \color{#9D38BD}{60^\circ} {\dfrac{3}{2}\pi}
Answer: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{60^\circ}{360^\circ} = \dfrac{3}{2}\pi \div A_c$ $\dfrac{1}{6} = \dfrac{3}{2}\pi \div A_c$ $A_c \times \dfrac{1}{6} = \dfrac{3}{2}\pi$ $A_c = \dfrac{3}{2}\pi \times 6$ $A_c = 9\pi$